A Non-Abelian Variation on the Savvidy Vacuum of the Yang-Mills Gauge Theory

Details A Non-Abelian Variation on the Savvidy Vacuum of the Yang-Mills Gauge Theory A Non-Abelian Variation on the Savvidy Vacuum of the Yang-Mills Gauge Theory

1993-12-17

arxiv.org/abs/hep-lat/9312069v1

Phys.Rev. D49 (1994) 6849-6856

Physics

High Energy Physics

High Energy Physics - Lattice

9 pages, preprint BU-HEP-93-22

Scientific paper

10.1103/PhysRevD.49.6849

As a prelude to a truly non-perturbative evaluation of the effective potential in terms of lattice QCD, the one loop effective potential for a non-Abelian gauge configuration is calculated using the background field method. Through a non-trivial correlation between the space and color orientations the new background field avoids the possible coordinate singularity, ${\rm Det}B_i^a=0$, observed recently by Ken Johnson and his collaborators in their Schr\"{o}dinger functional study of the SU(2) Yang-Mills theory. In addition, since our ansatz generates a constant color magnetic field through the commutator terms rather than derivative terms, many of the technical drawbacks the Savvidy ansatz suffers on a lattice can be avoided. Our one loop study yields qualitatively the same result as that of Savvidy's.

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